Rolling mill gauge control method and apparatus including plasticity determination

ABSTRACT

For the provision of automatic gauge control for the on line control of the delivery gauge of a workpiece passing through at least one roll stand of a tandem rolling mill, it is desired to establish the plasticity of each workpiece in relation to each roll stand of the rolling mill for the entire length of that workpiece from the head end of the workpiece to the tail end of the workpiece. The plasticity of each workpiece is established to provide a desired gauge control operation in relation to that one roll stand.

tet H91 [4 1 Mar. 26, 1974 ROLLING MlilLlL GAUGE CONTROL METHOD AND APPARATUS KNCLIUDIING PLASTTCIITY DETERMIINATHON Richard Q. Fox, Pittsburgh, Pa.

Westinghouse lEIectric Corporation, Pittsburgh, Pa.

Filed: Nov. 6, 1972 Appl. No.: 303,726

Inventor:

Assignee:

US. Cl. 72/10, 72/16 int. CII B21b 37/00 lFieIId 011 Search 72/6-12, l6,

References Cited UNITED STATES PATENTS 4/1971 Smith, Jr 72/7 IONING CONTROL POSITION DETECTOR MILL ENTRY TEMPERATURE STATION CONTROL PANEL 3,574,280 4/1971 Smith, Jr 72/8 Primary Examiner-Milton S. Mehr Attorney, Agent, or Firm-R. G. Brodahl 5 7 ABSTRACT For the provision of automatic gauge control for the on line control of the delivery gauge of a workpiece passing through at least one roll stand of a tandem rolling mill, it is desired to establish the plasticity of each workpiece in relation to each roll stand of the rolling mill for the entire length of that workpiece from the head end of the workpiece to the tail end of the workpiece. The plasticity of each workpiece is established to provide a desired gauge control operation in relation to that one roll stand.

6 Claims, 5 Drawing Figures POSITIONING DETECTOR I Pmminmaa @974 SHEU 2 IF 3 GAUGE (HE) GAUGE 0) OPENING (SDREF) wOmOm 30m UNLOADED ROLL DELIVERY ENTRY PRESENT GAUGEWX) DESIRED GAUGE (HD) Y m B .F wtm wumom jom mm W E D wmw DER Wm W CELT. SRN E S E R D..

PRESENT GAUGE(H L0cK-0- GAUGE(HD) ROLLING MILL GAUGE CONTROL METHOD AND APPARATUS INCLUDING PLASTICITY DETERMINATION CROSS REFERENCE TO RELATED APPLICATIONS Reference is made to the following previously filed and related patent application which is assigned to the present assignee:

Ser. No. 215,743, filed Jan. 6, 1972 and entitled Gauge Control Method and Apparatus For metal Rolling Mills and filed by A. W. Smith and R. Q. Fox.

Reference is made to the following concurrently filed, on Nov. 6, 1972, and related patent applications which are assigned to the present assignee:

Ser. No. 303,723 entitled Rolling Mill Gauge Control Method and Apparatus Including Temperature and Hardness Correction and filed by A. W. Smith.

Ser. No. 303,721 entitled Rolling Mill Gauge Control Method and Apparatus Including Entry Gauge Correction and filed by A. W. Smith and R. Q. Fox.

Ser. No. 303,725 entitled Rolling Mill Gauge Control Method and Apparatus Including Speed Correction and filed by R. Q. Fox.

Ser. No. 307,724 entitled Rolling Mill Gauge Control Method and Apparatus Including X-Ray Correction and filed by R. 0. Fox.

Ser. No. 303,722 entitled Rolling Mill Gauge Control Method and Apparatus Including Feedback Correction and filed by R. Q. Fox and D. J. Emberg.

BACKGROUND OF THE INVENTION The present invention relates to workpiece strip metal tandem rolling mills and more particularly to roll force gauge control systems and methods used in operating such rolling mills.

In the operation of a metal or steel reversing or tandem rolling mill, the unloaded roll opening and the speed at each tandem mill stand or for each reversing mill pass are set up to produce successive workpiece strip or plate reductions resulting in work product at the desired gauge. Generally, the loaded roll opening at a stand equals the stand delivery gauge or thickness on the basis of the usual assumption that there is little or no elastic workpiece recovery.

Since the operator provided initial roll opening setup conditions, or the initial roll opening settings provided by an associated digital computer control system operative with model equation information to calculate the setup screwdown schedules for the respective stands of the rolling mill, can be in error and since in any event certain mill parameters affect the stand loaded roll opening during rolling and after setup conditions have been established, a stand automatic gauge control system is employed if it is necessary that the stand delivery gauge be closely controlled. Thus, at the present state of the rolling mill art, and particularly the steel rolling mill art, a stand gauge control system is normally used for a reversing mill stand'and for predetermined stands in tandem rolling mills.

The well known gaugemeter or roll force system has been widely used to produce stand gauge 1 in metal rolling mills and particularly in tandem hot steel strip rolling mills and reversing plate mills where experience has demonstrated that roll force control is particularly effective. Earlier publications and patents such as an article entitled Installation and Operating Experience with Computer and Programmed Mill Controls by M. D. McMahon and M. A. Davis in the 1963 Iron and Steel Engineer Year Book at pages 726 to 733, an article entitled Automatic Gage Control for Modern Hot Strip Mills by J. W. Wallace in the December 1967 Iron and Steel Engineer at pages to 86, US. Pat. No. 3,561,237 issued to Eggers et al. and US. Pat. 2,726,54l issued to R. B. Sims describe the theory upon which operation of the roll force and related gauge control systems are based. Attention is also called to US. Pats. 3,568,637, 3,574,279, 3,574,280 and 3,600,920 issued to A. W. Smith, which relate to roll force automatic gauge control systems. In referencing prior art publications or patents as background herein, no representation is made that the cited subject matter is the best teaching prior art.

Briefly, the roll force gauge control system uses Hookes law in controlling the screwdown position at a rolling stand, i.e. the loaded roll opening under workpiece rolling conditions equals the unloaded roll opening or screwdown position plus the mill stand spring stretch caused by the separating force applied to the rolls by the workpiece. To embody this rolling principle in the roll force gauge control system, a load cell or other force detector measures the roll separating force at each controlled roll stand and the screwdown position is controlled to balance roll force changes from a reference value and thereby hold the loaded roll opening at a substantially constant value. Hot strip mill automatic gauge control (AGC) including evaluation of roll force feedback information involves the combination of a number of process variables, such as roll force, screw position, and mill spring which are all used to evaluate the gauge of the strip as it is worked in each stand. In addition, an X-ray gauge is used on the strip as it passes out of the last stand to evaluate the absolute strip gauge produced.

The two gauge error detection systems that are commonly used are the X-ray and roll force. X-ray gauges can be placed between each stand, but they are expensive, difficult to maintain, and can detect errors only as the strip passes between stands. The roll force error detection system is much less expensive, and can be more easily implemented in relation to the operation of all stands, to detect errors in gauge as the strip passes between the rolls of a particular roll stand, providing immediate evaluation of desired corrections to the roll openings. The roll force system, however, provides only a relative evaluation of the gauge, since it measures the amount of gauge deviation from a reference gauge, such as the gauge at the head end of the strip.

A practical combination of the two systems uses rollforce feedback to calculate fast corrections to fluctuations in gauge, and an X-ray guage to evaluate the absolute gauge of the strip coming out of the last stand. The fast corrections are calculated from the roll force feed back, the stand screwdown position, and the modulus of elasticity of the rolling stand. The slower X-ray gauge evaluation calculates simultaneous corrections to several stands, so that the absolute value of the gauge may be brought to the desired value.

The output of both of these systems is a change in the position references supplied to the screwdowns of selected roll stands.

The following well known formula expresses the basic roll force gauge control relationship:

h SD F K where:

h loaded roll opening (workpiece delivery gauge or thickness) SD unloaded roll opening (screwdown position) K stand mill spring constant F stand roll separating force. Typically, the roll force gauge control system is an analog arrangement including analog comparison and amplification circuitry which responds to roll force and screwdown position signals to control the screwdown position and hold the following equality:

where:

AF measured change in roll force from an initial force SD controlled change in screwdown position from an initial screwdown position. After the unloaded roll opening setup and the stand speed setup are determined by the mill operator for a particular workpiece pass or series of passes, the rolling operation is begun and the screwdowns are controlled to regulate the workpiece delivery gauge from the reversing mill stand or from each roll force controlled tandem mill stand. By satisfying Equation (2), and the assumptions implicit in Equation (1), the loaded roll opening h in Equation (1) is maintained constant or nearly constant.

As the head end of the workpiece strip enters each roll stand of the mill, the lock-on screwdown position LOSD and the lock-on roll separating force LOF are measured to establish what strip delivery gauge G should be maintained out of that roll stand. As the strip rolling operation proceeds, the roll stand separating force F and the roll stand screwdown position value SD are monitored periodically and any undesired change in roll separating force is detected and compensated for by a corresponding correction change in screwdown position. The lock-on gauge LOG is equal to the lockon screwdown LOSD plus the lock-on force LOP multiplied by the mill stand spring modulus K. The workpiece strip delivery gauge G leaving the roll stand at any time during the rolling operation is in accordance with above equation (1) and is equal to the unloaded screwdown position SD plus the roll separating force F multiplied by the mill spring modulus K, The roll force determined gauge error GE in relation to a particular roll stand is derived by subtracting the lock-on gauge LOG from the delivery gauge G. The following Equations 3,4 and 5 set forth these relationships.

LOG LOSD K*LOF To provide steady state gauge error correction, the well known X-ray monitor gauge control system is usually employed to produce screwdown offset for the roll force control. In the monitor system, an X-ray or other radiation gauge sensing device is placed at one or more predetermined process points and usually at least at a process point following the delivery end after the last roll stand of the mill in order to sense actual delivery gauge after a workpiece transport delay from the point in time at which the actual delivery gauge is produced at the preceding stand or stands. The monitor system compares the actual delivery gauge with the desired delivery gauge and develops an X-ray gauge error as an analog feedback control signal to adjust the operation of the reversing mill roll force gauge control system or one or more predetermined tandem mill stand roll force gauge control systems to supply desired steady state mill delivery gauge. In this manner, the conventional monitor system provides for transport delayed correction of steady state gauge errors which are caused or which are tending to be caused by a single mill variable or by a combination of mill variables.

In operator controlled mills, some steady state gauge correcting operations can eventually be taken off the monitor system by screwdown recalibration, and the like, between similar workpiece passes if steady state gauge error tends to exist along the entire workpiece and persists from workpiece to workpiece. in this manner, some reduction is achieved in the length of off gauge workpiece material otherwise associated with monitor transport delay. Similarly, corrective monitor system operation caused by head end gauge errors can be reduced by changes in the operator or associated computer control system provided setup from workpiece to workpiece.

A background general teaching of stored program digital computer control system operation is set forth in a book entitled Electronic Digital Systems by R. K. Richards and published in l966 by John Wiley and Sons.

An additional detailed description of computer programming techniques in relation to the control of metal rolling mills can be found in an article in the Iron and Steel Engineer Yearbook for 1966 at pages 328 through 334 entitled Computer Program Organization for an Automatically Controlled Rolling Mill by John S. Deliyannides and A. H. Green, and in another article in the Westinghouse Engineer for January 1965 at pages 13 through 19 and entitled Programming for Process Control" by P. E. Lego.

A programmed digital computer system can be employed to make the gauge error correction screwdown movement determinations as well as to perform other mill control functions. The computer employs a programming system including an automatic roll force gauge control program or AGC program which is executed at predetermined periodic intervals to calculate the desired screwdown movement required at each roll force gauge controlled stand for gauge error correction including that stemming from roll force error detection at that stand.

SUMMARY OF THE INVENTION In accordance with the broad principles of the present invention, a system and method for controlling workpiece delivery gauge in a metal rolling mill employs means for detecting gauge error in the workpiece delivered from a given roll stand, and means for controlling the screwdown position of at least that one rolling stand of the mill in accordance with a predetermined relationship between said gauge error, the stand mill spring modulus and the workpiece plasticity for that stand, which plasticity is determined by calculation, for correcting the delivery gauge in relation to that given roll stand and this detected gauge error.

BRIEF DESCRlPTION OF THE DRAWINGS FIG. ll shows a schematic diagram of a tandem hot steel strip rolling mill and an automatic gauge control system arranged for operation in accordance with the present invention;

FIG. 2 illustrates the typical mill spring curve and workpiece reduction curve for a given rolling mill stand and the operation of that roll stand for reducing the gauge of a workpiece passed through the roll stand;

FIG. 3 illustrates, in relation to the mill spring curve and the workpiece reduction curve, the effect of a correction made to the screwdown position setting for changing the unloaded roll opening of a roll stand to provide a desired change in the workpiece gauge delivered from that roll stand.

FIG. i shows an illustrative gauge error detection operation in relation to the initial lock on conditions at the head end of the workpiece.

FIG. 5 shows a schematic illustration of the plasticity determination operation in accordance with the present invention.

DESCRIPTION OF Til-IE GAUGE CONTROL SYSTEM AND ITS OPERATION There is shown in FIG. ii a tandem hot strip steel fin ishing mill llll operated with improved gauge control performance by a process control system l3 in accordance with the principles of the invention. Generally, however, the invention is applicable to various types of mills in which roll force gauge control is employed.

The tandem mill 1111 includes a series of reduction rolling stands with only two of the stands Sll and S6 shown. A workpiece l5 enters the mill ill at the entry end in the form of a bar and it is elongated as it is transported through the successive stands to the delivery end of the mill where it is coiled as a strip on a downcoiler T7. The entry bar would be ofknown steel grade class and it typically would have a known input gauge or thickness of about ll inch and a width within some limited range such as inches to 80 inches. The deliv ered strip would usually have approximately the same width and a thickness based upon the production order for which it is intended.

In the reduction rolling process, the successive stands operate at successively higher speeds to maintain proper workpiece mass flow. Each stand produces a predetermined reduction or draft such that the total mill draft reduces the entry bar to strip with the desired gauge or thickness.

Each stand is conventionally provided with a pair of backup rolls 119 and M and a pair of work rolls 23 and 25 between which the workpiece 115 is passed. A large DC drive motor 27 is controllably energized at each stand to drive the corresponding work rolls at a controlled speed.

As previously described, the sum of the unloaded work roll opening and the mill stretch substantially defines the workpiece gauge delivered from any particular stand in accordance with Hookes law. To vary the unloaded work roll opening at each stand, a pair of screwdown motors 29 (only one shown at each stand) position respective screwdowns 31 (only one shown at each stand) which clamp against opposite ends of the backup rolls and thereby apply pressure to the work rolls. Normally, the two screwdowns 31 at a particular stand would be in identical positions, but they can be located in different positions for strip guidance during threading, for flatness or other strip shape control purposes or possibly for other purposes.

A conventional screwdown position detector or encoder 33 provides an electrical signal representation of screwdown position at each stand. To provide an absolute correspondence between the screwdown position and the unloaded roll opening between the associated work rolls, a screwdown position detection system which includes the screwdown position detector 33 can be provided and calibrated from time to time.

Roll force detection is provided at each of predeter mined stands by a conventional load cell 35 which generates an electrical analog signal in accordance with the stand roll force. At the very least, each roll force controlled stand is provided with a load cell 35 and in many cases stands without roll force gauge control would also be equipped with load cells. The number of stands to which roll force gauge control is applied is predetermined during the mill design in accordance with cost-performance standards, and increasingly there is a tendency to apply roll force gauge control to all of the stands in a tandem hot strip steel mill. In the present case, a roll force gauge control system is assumed to be employed at each of the stands.

Conventional motorized sideguards 37 are located at predetermined points along the mill length. The sideguards 37 are operated during mill setup on the basis of the widths of the upcoming workpiece l5 thereby defining the sides of the workpiece travel path for guidance purposes.

The process control system 13 provides automatic control for the operation of the tandem mill 1111 as well as desired control for associated production processes (not indicated) such as the operation of a roughing mill. The process control system l3 can include a pro grammed process control digital computer system which is interfaced with the various mill sensors and the various mill control devices to provide control over many of the various functions involved in operating the tandem mill llll. According to user preference, the con trol system l3, can also include conventional manual and/or automatic analog controls for selected process control functions.

On the basis of these considerations, automatic gauge control system 39 can include a digital computer system operative to provide the finishing mill on-line roll force gauge control function, such as a PRODAC 2000 (P2000) sold by Westinghouse Electric Corporation. A descriptive book entitled PRODAC 2000 Computer Systems Reference Manual has been published in 1970 by Westinghouse Electric Corporation and made available for the purpose of describing in greater detail this computer system and its operation.

There is disclosed in the above-referenced previously filed patent application Ser. No. 21.5,743 the logic flow chart of an illustrative automatic gauge control system suitable for operation with the plasticity determination operation of the present invention, for example at step -40 of the flow chart shown in FIG. tiA the plasticity is calculated. It should be readily understood by persons skilled in this art that the present invention is also suitable for operation with other well known automatic gauge control systems Where a determination of workpiece plasticity is desired for controlling the delivery gauge of a workpiece strip passed through at least one stand of a rolling mill.

The digital computer processor can be associated with well known predetermined input systems typically including a conventional contact closure input system which scans contact or other signals representing the status of various process conditions, a conventional analog input system which scans and converts process analog signals, and operator controlled and other information input devices and systems 4311 such as paper tape teletypewriter and dial input systems. it is noted that the information input devices 431 are generally indicated by a single block in FIG. ll although different input devices can and typically would be associated with the control system. Various kinds of information are entered into the control system through the input devices 41 including, for example, desired strip delivery gauge and temperature, strip entry gauge and width and temperature (by entry detectors if desired), grade of steel being rolled, plasticity tables, hardware oriented programs and control programs for the programming system, and so forth. The principal control action outputs from the automatic gauge control or AGC system include screwdown positioning reference commands which are applied to respective screwdown positioning controls 55 for operating the screwdown motors 29 for screw movement, and speed control signals which are applied to the respective speed and tension control system 53 to cause a change in drive speed to compensate for a change in thickness being made by a screwdown movement.

Display and printout devices Sil such as numeral display, tape punch, and teletypewriter systems can also be provided to keep the mill operator generally informed about the mill operation and in order to signal the operator regarding an event or alarm condition which may require some action on his part. The printout devices are also used to log mill data according to computer log program direction.

Generally, the AGC system uses Hookes law to determine the total amount of screwdown movement required at each roll force controlled stand at the calculating point in time for roll force and gauge error correction, i.e., for loaded roll opening and stand delivery gauge correction to the desired value. The calculation defines the total change in the unloaded roll opening required to offset the gauge error causing condition.

During rolling operation, the on line gauge control system operates the stands to produce strip product having desired gauge and proper shape, i.e., flat with slight crown. On line gauge control is produced by the roll force gauge control loops at the stands and the previously noted X-ray monitor gauge control systems.

In the monitor system, the X-ray gauge 17 produces the X-ray gauge error or deviation signal which indicates the difference between actual strip delivery thickness and desired or target strip delivery thickness. in other cases, it may be desirable to employ an absolute thickness measurement X-ray gauge signal to form a basis for monitor control actions or, more generally, for screwdown offset control actions.

To effect on line gauge control in the closed loops, the AGC system operates at predetermined time periods such as every 2/10 second with the screwdown position detector and load cell provided signals from each stand as well as the X-ray gauge duration signal to determine the respective stand screwdown adjustment control actions required for producing desired strip delivery gauge.

In FIG. 2, linear approximations of the roll stand characteristic curves are shown to illustrate the application of ll-lookes law to a rolling mill stand and to illustrate the basis upon which the on line gauge control system provides improved gauge control, accuracy and stability and other operating benefits. A mill modulus characteristic or mill spring curve defines the separation between a pair of workpiece reducing mill stand work rolls as a function of separating force and as a function of screwdown position. The slope of the mill spring curve W0 is the well known mill spring modulus or constant K which is subject to variation as well known to persons skilled in this art. When a correct screwdown calibration is known and the screwdowns are posisioned such that the empty work rolls are just facing, the unloaded screwdown zero position is defined. The workpiece deformation characteristic or re duction curve 102 is shown. The entry gauge H of the workpiece passed through the roll stand is reduced to the indicated delivery gauge H as defined by the intersection of the mill spring curve 100 and the product reduction curve 102 to establish the stand roll force required for the indicated operation. The unloaded roll opening, sometimes called the screwdown because of the screw-and nut system used for adjusting the roll opening, is the gauge that would be delivered if there were no roll separating force. As the force increases with a constant roll opening, the delivery gauge increases, since the mill deflects as shown by hte mill spring curve 100. If no force was exerted on the product being rolled, the gauge would not be reduced and the delivery gauge would be equal to the entry gauge. When the roll force increases, the product is plastically deformed and the delivery gauge decreases. The slope of the mill spring characteristic line is called the mill modulus (K) and the slope of the product reduction characteristic is called the product plasticity (P). The delivery gauge is determined by the equilibrium point at which the force exerted by the mill is equal to the force required to deform the product. Changes in entry gauge and product hardness result in a change in roll force and delivery gauge. The automatic gauge control moves the screwdown to correct for these gauge changes. The main advantage of the roll force gauge control system is its ability to detect changes in gauge the instant they take place, as the product is being rolled in the stand. A shift in delivery thickness can be caused by a change in entry thickness or a change in hardness (usually caused by a change in temperature). This change in delivery gauge is immediately detected by monitoring the roll separating force of the roll stand.

When the screwdowns are opened (positive movement) the unloaded roll opening increases as reflected by a change to the right in the graphical location of the mill spring curve lltltl such that the theoretical spring curve intersect equals the new unloaded roll opening. With screwdown closing, the mill spring curve is shifted to the left in a similar manner.

At any particular screwdown position and with correct screwdown calibration, the stand workpiece delivery gauge H equals the unloaded roll opening as defined by the screwdown position SDREE plus the mill stretch (F*K) caused by the workpiece. If the screwdown calibration is incorrect, i.e., if the number assigned to the theoretical roll facing screwdown position is something other than zero because of roll crown wear or other causes, the stand workpiece delivery gauge l-l then equals the unloaded roll opening plus the mill stretch, plus or minus the calibration drift.

The amount of mill stretch depends on the product deformation characteristic or reduction curve M2 for the workpiece as shown in FIG. 2, the reduction curve I02 for a strip of predetermined width represents the amount of force F required to reduce the workpiece from the stand entry gauge (height) I-I The workpiece plasticity P is the slope of the curve W2, and the curve W2 is shown as being linear although a small amount of nonlinearity would normally exist.

Desired workpiece delivery gauge H is produced since the amount of force F required to reduce the workpiece from E to H is equal to the amount of roll separating force required to stretch the rolls to a loaded roll opening l-I i.e., the intersection of the mill spring curve MW at an initial screwdown opening SDREF indicated by mill spring curve iltliti and the workpiece reduction curve W2 lies at the desired gauge value I'l As shown in FIG. 3, if the actual stand present gauge Hx is not the same as the desired gauge l-I there is a gauge error GE to be corrected. This condition can be corrected by changing the provided screwdown position reference SDREF to the stand, such that a new mill spring curve Mi t becomes operative to result in the desired gauge l-l being delivered from the roll stand and the gauge error GE is now removed.

It is known in accordance with the teachings of above referenced US. Pat. No. 3,561,237 that the required corrective screwdown adjustment ASD to correct a stand delivery gauge error GE is equal to the product of that gauge error GE times the sum of the ratio of the workpiece plasticity P for that same stand with the mill spring modulus K for that same stand and one, as follows in relation to stand (N):

ASDUV) exit GE(N) [P(N)/MN) The stand N exit gauge error determined by the roll force system at stand (N) is established by the relationship of above equation (5) as follows:

In reference to FIG. d, in general the workpiece strip gauge error delivered by a given stand, and as determined by the sensed operational variable at that same stand, is in accordance with the roll force system relationship shown in above equation (8). The exit gauge error leaving stand (N), for example, equals the sum of a first quantity, which is the difference between the presently measured screwdown position SD(N) and the initial lock on screwdown position L()SD(N), and a second quantity, which is the determined mill spring modulus K(N) times the difference between the presently measured roll separation force F(N) and the initial lock on roll force LOF(N).

DESCRIPTION OF EMBODIMENT OF PRESENT INVENTION In general, the plasticity P(N) of a workpiece strip in relation to roll stand (N) of a rolling mill is a function of the strip width, temperature, gauge and hardness. The plasticity P(N) for typical roll stand (N) must be accurately determined in order to remove and correct by screwdown adjustment at stand (N) the delivery gauge error it is desired to correct at stand (N). For this purpose, the present control system including the digital computer is operative to calculate the plasticity of the workpiece strip at each roll stand every 0.2 second. Since the workpiece plasticity is a measure of the change in thickness caused by a compressive roll force, it is calculated by the following relationship:

P(N) Draft (N)/Force (N) P(N) Entry gauge (N) Exit gauge (N)/Roll force Since the entry gauge to stand (N) is equal to the exit gauge leaving previous roll stand (I I1), the following relationship can be established:

Exit gauge (N-l Entry Gauge (N) I) This permits the following modification of above equation (10) for plasticity:

P(N) Exit gauge G(N-U-Exit gauge G(N)/Roll Force P(N) The following workpiece volume mass flow relation ship between the stand speeds and delivery gauges must be provided for proper passage of a workpiece through the plural stands of a tandem rolling mill:

(1 Where:

G(I) is the delivery gauge leaving the first roll stand S(l) is the operating speed of the first roll stand G(N) is the gauge leaving stand (N) S(N) is stand (N) operating speed G(LS) is the last stand delivery gauge S(LS) is the last stand operating; speed.

Since the X-ray device positioned after the last stand is operative to measure the last stand delivery gauge XG(LS), the following relationships can be established:

Using the well known mass flow relationship set forth by above equation (13). Now if the quantities of equations l4) and (15) are substituted into above equation (12), the following relationship for plasticity P(N) at stand (N) will result:

The latter equation can be rearranged as follows:

The width of the workpiece strip passing through the roll stands of a tandem rolling mill is assumed to remain substantially constant for the purpose of the determination of workpiece plasticity for each stand of the rolling mill.

In reference to FIG. 5, there is shown a portion of a tandem rolling mill including the last roll stand (LS), an earlier roll stand (N) and then a previous roll stand (N-l with the workpiece strip 15 moving in the direction indicated by the arrow. The X-ray device 500 provides an X-ray gauge deviation in relation to absolute gauge error leaving stand (LS). At block 502 the desired gauge reference is added to the X-ray deviation such that the actual X-ray measured gauge XG(LS) is supplied to block 504. At block 504 the plasticity P(N) for stand (N) is calculated using above equation (17). At block 506 the exit gauge error G(N) leaving stand (N) is calculated in relation to above equation (5 with the understanding that block 506 includes a memory function such that the lock on values of the screwdown LOSD(N) and the roll force LOF(N) are remembered 'as required in this regard. At block 508 there is deter- UIN w 0001 4 E DAT:& FILE 0008 A 3 0003 TYL 000 0006 0006 a 0007 O 0008 o 0009 0 001.0 0011 Q 0012 0013 1000 001M FILE 91% 1000 0015 FL IZE 0% 1001 0016 FHPFLS BRU 1002 001.7 RVPFLS HRH 1003 0013 F'XDCEN ERG 100' 0019 REVS T B W I005 002G REFENC R 1000 D32: EtE't'E sea gm" 535g sfiifi? 62%.: 2308 0033 CAL- I009 202 B 100A 0025 ENCNB WW 1008 0026 w'KDATA 696 100C 0927 CL E W 1000 0028 ZERBCG 0R8! 100E 0029 ENBREF BRu F 0030 em: 1010 0031 BINPT B14 1011 0032 CALP'LAG 81% 1012 0033 PFLCAL ERG I013 003!) DREFIL BRG 101 0035 PRBLBC Ems mined the stand (N) screwdown position correction SD(N) required to remove this same stand (N) gauge error, and this utilizes above equation (7) for this purpose.

The typical AGC control program is written as a loop operation such that one set of coding processes all of the roll stands, and every time the program operates through the loop a calculation is made when appropriate for each of the roll stands in relation to the gauge 10 error and the plasticity determination for adjusting each roll stand screwdown position as desired to correct the delivery gauge error at that roll stand.

GENERAL DESCRIPTION OF INSTRUCTION PROGRAM LISTING tinghouseElectric Corporation for real time process" control computer applications. Many of these digital computer systems have already been supplied to customers, including customer instruction books and descriptive documentation to explain to persons skilled in this art the operation of the hardware logic and the executive software of this digital computer system. This instruction program listing is included to provide an illustration of one suitable embodiment of the present control system and method that has actually been prepared. This instruction program listing at the present time has been partially debugged through the course of practical operation for the real time automatic gauge control of a tandem rolling mill, but it is understood and well known by persons skilled in this art that most real time process control application programs contain some bugs or minor errors, and it is within the routine skill of such persons and takes varying periods of actual operation time to identify and correct the more critical of these bugs.

lAGC DATA FILE! MBDIF'IED 1/26/72 THE FQLLBWING IS A CBMFLETE LISTING 6? THE AGE DATA FILE E T IES! 9 NUMBER 81 WSRDS I\l THIS DATA FILE not RELeADDWuBF FWDo RBFILES IA n01 RELoADDQofW REVv ROFILES BIA 04-1 RELQADDM 9F FIXED PSI T CBNST S U 1 ENCQDE EVBLUTIBN CBUNT 0*; "E IN ENCQDE LNWS 0: E C DE CALIBQA IQM 8M? MS) 9-9 M1 1 INSYQUTG IN UT EJCaQEAOING 0-91 SPEED PAYTERN Ill-B eel CLQSED LBBP REGISTER lLllQER 0M ZERB ERRBR C6 I INCLUDED 3:: REF-"o IN ENGINEERING UNITS (2 N05) 001 LECuGF BINARY PT IN FIXED PTOWDSI QM. DRIVE IN CALIBRATIBJ FLAG 1 AUXILIARY 500 RQFILE IMDIC TR 5N1 PRE ENT ACTIBN Pla BF SwDoPRDFIl-E A C D TA ILE 0096 0097 0098 0099 0100 0101 0102 0103 01047 0105 0106 0107 0108 D109 D110 D111 0135 0136 0137 0138 0139 01 00 01 11 01 12 0103 011: 01 15 0106 0107 0108 OMB 0150 0151 015a 0153 015A 0155 0156 0157 0158 D159 0 HEADEND LIMIT HANCBHF o HAXDELTA MAXK NAXS D MGR 0 MBVEUP MPH O NEGLH'IT D NDYCALIB o BLDREF Q BTHER Q PLASI PLSCHL,

0 PBSITIBN PBSLIM PULSE o RDIAMREG D RDLLDIAM SDLB SDLBACT 42 SCREW SELFWR 0 SEPARATE SKIDS O SKIDSIZE.

SPEED SPEEDLB 0 SPEEDMPS TAILCBM TAILTIHE.

o TCBHPV L a TCBMSBS 0 TEMRFBRC THIC XINT

FXDDFF XDNUL FXDSHF BPTFL-GS REVLIM VWDLIM SPEEDS MAXRM' PRDFWA DRE 0RD DRE DRE BRG ERG ORG

EUE

an 0 1 0M M1 an (m1 UM 0M. (M1 M1 01 CW1 00; OM OM M1 0M,

GAUG RRBR FEAQ FDR HEAD END 0 51'9" MILL FIBDULUS VDR 5TAND FEEDDACK CBRRECTIDN CDE ICIENT INPUT CHANNEL FDR PULSE TACH REFERENCE FBR PBSITIDN PROGRAM PDSITIVE LIMIT 3N STAND MOVEMENT CURRENT PULSE READING ROLL D!ANETER REGISTER RBLL DIAMETER READ B? THIQ PROGRAM SCREW DBHN LBCK 5N ACTUAL SD LBCKuBN SCREW FEEDBACK SELBYN PBWER CD LDCAYI N DISTANCE TB NEXT STAND 1N ILLWETERS DELTA '3 BF PREVIDUS SCAN LEN TH 8V SKID MARK MILL REVQLUTIBNQ PER MINUTE SPEED LDCK-JDN MAIN DRIVE SPEED IN WETERS/SEC.

TAU, END CDMPENSATIDN FLAG TAILEND CBH ENSATIBN TRANSPORT TIME Pesmemma 'zrazuc'e FER TEMP cewzusmerv TEM CBHPENSATIDN 0N STRIP BUT 9F 51' TEHPEICBRRECTIBN F-BRCE CALCULATED DUTPUT GAUGE INTEGRAL PART BF XRAV CBRRECTIDN THIS SECTIBN IS REDLHRED FOR ALL DRIVES IN THE EVSTEMI FIXED PTa HULTo FACTBR IDRA! 0X CDDE SPEED L1H: DP'IIDN FLAGS REVERDE PBSITIBN LIHT PBRWARD POSITION LIMIT FBRNARD/ EVE BE BREED LIHITB IMUM BBIYIDN REFo IN ENCQUNITI FDWARD PRDPILE A PRDP'IL-EZ PBINT PRBP'ILE PBYNT F RBF 'XLZ PBINT ADC TABLES A230 A235 A236 A237 A230 A239 523A M235 4023C A230 4232 423 M150 2M A2 E 63 25h 2M5 32110 351E 3E1? SE20 3521 3522 3523 SE21? GOOOOOOOU A0 82 m 90 ca A0 82 0333 033 0336 0336 0337 0338 0339 03 W 03M 0302 03 8 02% 9305 03M: 03 67 0308 0309 0380 0351 0352 02-793 035: 0355 0356 0357 035a 0389 0300 0361 0362 0363 036 0365 0366 0367 0368 0369 0370 0371 0372 0373 037A 03% 03176 0377 0378 0379 0380 IGLBGP LBBFCHNB 0 AGCNUH ABCFAT 0 AGCREG 0 AGCMREG O AGCPATI 0 BIYPATI 0 BIT ATE 0 BITPAT3 a BIT TA o CDHF'FPCT CBUNTER DELAY GAGETBLE DAT DAT DAT DAT OAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT 0A1 YTla 0R0 DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT 510E DAT DAT DAT DAT DAT DAT EGU DAT DAT DAT DAT DAT DAT DAT DAT .30 K5 'AUTBHATIC GAUGE CGNTRBL' To o 0 00000 00 o 0000 THHB DATA MUST BE XHDDO! XBDD MBDIPIEDI THI PFIGDRAH CDNTRDLS TH! GAUGE OF THE HILL BY THREE WRBCESSES! DIRECT ACTHW BASED ON ROLL FORCE CALCULATIQNS 0F THE GAUGE ERRBR; FEED FORWARD T0 HANDLE SKID MARKS! AND FEED BACK TB HANDLE STANDS WHICH GB 01' 0 LIMITSo THE PROGRAM AL50 BUT UTS A CBRRECTIBN T THE LDBPE SI DEFINED 0V PRBDRAHHER BUT UT SYSTEM FBR LODPERS 0 F00 DIGITAL SYSTEMS 1 FDA ANALBG SY5TEM5 eena coaazc'rmu BUI'PUY CH- NuH E TAIL D 090% CC! BIT PATTERN PDRCEE.

XRAV CBHPn WEIGHTING FACTOR IN CT T000 FOR UPDATING XRAV INTEGRAL PEEDFBRHARD TIME T0 ADVANCE HBVXN 0 SCREWS IN TENTMB 0P SECONDS Pam'rm m FBRCE TABLE TABLE 6? ACCEPTABLE LDCK 0N amass m m aao ADJUBT m FIELD AUYB 'TAT IE GAUGE BEEC ZIEE'E BEEF SE AC BEAD EE IE OOCB OSFA

FFE?

1000 PODS I CE 0200 AA 22 CDNTRD 0 DO A 0381. DAT Q o 00 A 0382 DAT D 0 0D A 0303 DAT Q 0 Do A DSIAA DAT O D 00 A 03% DAT D J 00 A 03% PM 0 0 00 A 0387 DAT 0 03M 0 ARAT GA a G a A O (713 A 0309 GAU EDI T DAT XIEOQI u N n W 0 A owe TACT R: O T 12o HILL, wmme ATDTA calm A DR 0 1A A egg; AACTDRE DAT 2O MILD DMIND MOTH can: I'MCITTDR O 0 D 00 A 0393 INDEXSIZ DAT 9 03% A ACCELTRATIDA CBRRECTTDN AAcTDR. 03% A THID CONTANT IS A MLTIAATER F051 03% O DETERMINING THE AECELERA IDN EDN 0397 A TEETH: TD GDED 0 CD A 3% 02 DAT 200 0399 XRAY CIIRNEETIDN IAEADTHEM PRDPA MOD W INTEDAIATDR CBNSTANTD MDT 0 TD E ADJUSTED IN FIELD 2 2 A 0002 KTABLEF' DAT KTABLE PDINTEI' I TD K TABLE 0 DA A M03 LBWNUH DAT X I ADDI- I A D LDcA 0N DAueE cc: AEDISTER o 00 A 0 :05 LDDPPATU DAT D DADA 0 GDP R RA SE CCD P D 05 A 0A0? LDBPREGU DAT 5 ta E I TERM DADA A WA ER AAIsE cw RE IDTER o 00 A DADD LDDPNsKu DAT D 0M0 A LBDT'IER RAISE CCB MASK 6 DC A A1; HAXAEDDW DAT 1a 0MB A MAXIMUM INITIAL XFTAY GAUGE DEVA D013 0 BEFDRE )(RAY MDNA HDLD DCCURS 0AM A IN ENCDDER UNITS o 19 A 0M5 MAXQAGE DAT 5 MIA A MAXIMUM BABE IN PERCENT 5 M A 0M7 MAXWXDTH DAT 1530 OMB A MAX WIDTN 0F HILL PRODUCT! 0M9 A IN MILLIMETEM o 00 A DAED MDNPATDF DAT o MDNA MALD L IDHT DFF ccD PATTERN 0 Do A M21 NDNDFPAT DAT o MBNA LIGHT BFF CcD PATTERN 3 0B A M22 MNDADREG DAT xv 5 m W23 0 XRAY MBNA NDLD CCI BIT PATTERN 7 E7 A ADA MINGIAGE DAT 25 W25 A MINIMUM GAGE IN PERCENT 0 02 A was NBNDUAND DAT a 0A2; A MDNITBR DEADDAND m a: D 00 A DADA MDNBNNSA DAT X'IDDD DATED A MDNITDR DN LIGHT NASA 0 00 A oAao MDNDNPAT DAT x 1000i 0 01 A OM11 MDND UM DAT X ADDI A 5A3? A MDNITBA DN LIGHT PATTERN I) DA A M33 MDNBNREG DAT A MIN 0 MDNI T051 0N LIGHT REGISTER 1 00 A was MDNnAsA DAT xuom 3M6 A MBNITBR HELD LI HT CCU NASK I Do A M37 "IDNPAT DAT x 1001 DADA A MDNITBN HDLD LIGHT ccD PATTERN D 0A A mew NDNAED DAT A Q D MDNITDA HELD LIGHT ccfi REGISTER o 07 A OMAI NEIEFDRVS DAT '7 aAAa A NUMBER 9V DRIVES A Do A QAAD DNBITPAT DAT xmool DAAA A WAY MDNITDR BN cc: 5.1T PATTERN 3 53 A WW L WAT 100D MAXIMUM T LASTICITY VALUE 0 DA A DAAA P'EASTLD DAT 1O "TINIMUA P AsTIcITv VALUE 0 DO A 0M7 PDSITN DAT o DAAA A TEMPDRARY REFERENCE FDR STRTFOS 0 DA A 0M9 PRDDRAMN DAT A MED A NUMBER AF Tm FDR XRAY sCAN 1 2C A DAB: PULFREV DAT 300 M DE A PULSES PER REVBLUTIDND 3 CE A MED RDMTWED DAT X'IBCEI REGISTER LBCA FDR RDLJGHER THICKNESS 2 00 A DADA GAGEF'AT DAT 10200 4 A MICK 8N GAUGE CCI BIT PATTERN 0A A DADA SCRDELAY DAT 1D DAD? ESTIMATE DP TIME FDR SCREWS TD PBS DASII A IN TENTND BF DECDNDS D 00 A DADA sPDcDN DAT Q DAAQ A SPEED CDARECTTDN CDNETTANT IN mm 5 50 A 9AM EIPEEDTAB E00 A! 0 0A A oAAa WT A 0 DO A 0M3! DAT O 0 DO A 0M3 DAT D r. 00 A M63 DAT 0 0 0D A 0M3 DAT D n 00 A {New MT 0 o 00 A 0 :63 DAT D DADA A 0MB A ACCELENATIDN CDRRECTIDN TABLE (TENS) 0 00 A DAM STDMBNDT DAT X 1000' STAND ITDNITDR SELACCI BIT PATTERN CHAD? AA FEED FDR'WADD TADATABLE LDC-1 0M8 A 0 9.7 A DAM TDDKID DAT XI 7' 0WD AA THICKNESS CI REGA 3 DA A 0W1 TNRDGu Tzmu x1 IBDAT AUTBWATXC GAUGE QEB IIEBC 35.61 3E0? 31563 3E6 M05 SE00 3%? SE68 3E69 STEM 3156B 350C EEBM ccmmm,

3 DE A 0 031 A OOOOOOOOOOOQQ O 3 CO0 00 0072 0 72! 0470 0W5 0076 0 :77 0078 3479 0080 0081 0082 0003 0 8 0W5 OM36 0687 0 88 0689 0090 0093 0093 0093 0090 0095 0095 0095 0495 0095 0095 0095 0095 0095 0095 0495 0090 0090 0097 0090 0099 0500 0501 0502 0503 0500 0505 0500 0807 0508 0509 0510 0511 0512 0813 05!. 0515 0516 0517 3516 0519 0520 0581 0522 0523 052 0 0525 0526 0527 0528 0529 0530 0531 0532 0533 0530 0535 0530 0537 05310 0539 05 m 0501 0502 05 :3 05M) 0505 0500 0507 0508 0509 0550 0051 0553 05511 0550 0555 0556 THREE? TINEF'UNC 0 UNXTEPHH O WIDTHRED o XRAYIREG o XRAYEREG o XRNDTIME 0 XSED ITS o XSEL E 0 RDNREG o AGCHASK 0 AVERDEV CAM CALE INDEX O LASTSTND mn LIM LIME NPHLS 0 MBNITIME 0 NASSFLBW NBMI AL, LD XZE DUT LI DRCNTDEV SETU N 0 SAVEC EQU DAT DAT DAT

DAT

DAT

DAT

DAT

DAT

RPT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT Edi DAT DAT

DAT DAT DAT DAT

DAT DAT DAT DAT DAT DAT DAT DAT DAT DAT

DAT

DAT

DAT DAT DAT DAT DAT DAT

DAT DAT DAT DAT

DAT

DAT

DAT

O O O O 0 O0 0 0 00 0 O C) O O0 O00 000 O O O 00 O O 000000000000 N XRAY nawren csmzcnaw 021cm new \IUNDER 9F zwcsozn uws wan MLLIHET MDTHA cc; was

ZRAV STATUS CC! 5!? AT TIME DELAY IN 5/10 SECS AFTER WHICH XRA BNXTBR BECOMES ACTWELY NVBLVED IN GAUGE CDNTRBLo XRAY SELECTED CCl BIT PATTERN XRAV SELECTED CCI REDo XRAY NSNITBR 0N CCX REG.

SPARE QPARE SPARE SPARE SPARE SPARE SPARE SPARE SPARE SPARE SPARE SPARE THI DATA IS INTERNAL T0 PROGRAM LIGHT CCB 1ASK AVERADE GAUGE DEVIATION STAND CALIBRATIDV STATUS AS DETERHIN BY THE PEEDBACK RBUTYNE STAND CBHF ENSATIBN FACTBR INTERNAL TABLE I DEX AVERAGE GAUGE DEVIATIBN HEIGHT FACTB TEMP ETBRAGE DE DE DBLE PRECISXON DRXVE NUMBER CALCULATED BY PRDGRAN NEW GAUGE XRAY GAUGE DEVXATIBN 1N ENCBDER UNIT HAFIDNESS HEAD END XHFSRTANCE WEIGJTING FACTOR PBI TER T0 ACCELERATIBN CBRRECTX TABLE (SPEEDTBL) GAU E THICKNESS 0F LAST STAND PRDDUC LAST BTANS STRX VIELBCITY NBNITBR TRANSFER? TIME DELAY THICHLAST)" SPEEDM SILAST) K FAETBMMFACTBREnW/NNAXMK/iOD NBNINAL GAUGE 0L0 SAMPLE SIZE LAST STAND REQUIRED FEEDBACK PERCENT DEVEATIDN RETURN ADDRESS FDR FEEDBACK ROUTINE C REGISTER STBRAGE 

1. A gauge control system for a rolling mill having at least a first roll stand and a second roll stand operative to reduce the gauge of a workpiece passed through said rolling mill and including a device for measuring the gauge of said workpiece leaving the rolling mill, said system comprising: means for determining the plasticity of said workpiece for each of a plurality of segments along the length of said workpiece in relation to said second roll stand in accordance with a predetermined relationship including for each of said workpiece segments said measured gauge of said workpiece, a first speed related to the workpiece, speed leaving said first roll stand, a second speed related to the workpiece speed leaving said second roll stand and the roll force of said second roll stand, and means for controlling the roll opening of said second roll stand for each of said workpiece segments during the passage of said workpiece in accordance with said plasticity determined for the same workpiece segment.
 2. The gauge control system of claim 1, with said plasticity being determined for each said workpiece segment in accordance with the relationship: P(N) (XG(LS)*S(LS)/F(N)) * l/S(N-1) -1/S(N)) Where P(N) is the determined plasticity, where XG(LS) is the measuRed gauge, where S(LS) is related to the speed of the workpiece leaving the rolling mill, where F(N) is the roll force of the second roll stand, where S(N-1) is said first speed, and where S(N) is said second speed.
 3. The gauge control system of claim 1, with said means for controlling the roll opening of said second roll stand for each of said workpiece segments being operative in accordance with the relationship: Delta SD(N) GE(N)* (K(N)/P(N) + l) where Delta SD(N) is the adjustment to be made in the roll opening of said second roll stand, where GE(N) is the gauge error of the workpiece leaving said second roll stand, where K(N) is the mill spring modulus of the second roll stand, and where P(N) is the determined plasticity.
 4. A method of controlling the workpiece gauge leaving a rolling mill having at least a first roll stand followed by a second roll stand and being operative to reduce the gauge of a workpiece passed through said rolling mill and in relation to a measured gauge of said workpiece leaving said rolling mill, the steps of said method comprising: determining the plasticity of said workpiece for each of a plurality of workpiece segments along the length of said workpiece in relation to said second roll stand in accordance with said measured gauge, the roll force of said second stand and the speed of said workpiece in relation to each of said first and second roll stands, determining the gauge error for each of said workpiece segments of said workpiece leaving said second roll stand, determining a correction for application to said second roll stand in relation to each of said workpiece segments during the passage of said workpiece in accordance with a predetermined relationship between said gauge error and said plasticity of said first workpiece, and controlling the operation of said second roll stand in relation to each of said workpiece segments in accordance with said correction.
 5. The method of claim 4 with said plasticity for each of said workpiece segments being determined in accordance with the relationship: P(N) (XG(LS) * S(LS)/F(N)) * (1/S(N-1) - l/S(N)) where P(N) is the determined plasticity, where XG(LS) is the measured gauge, where S(LS) is related to the speed of the workpiece leaving the rolling mill, where F(N) is the roll force of the second roll stand, where S(N-1) is related to the speed of the workpiece leaving the first roll stand, and where S(N) is related to the speed of the workpiece leaving the second roll stand.
 6. The method of claim 4, with said correction for each of said workpiece segments being determined in accordance with the relationship: Delta SD(N) GE(N)* (K(N)/P(N) + l) where Delta SD(N) is the correction, where GE(N) is the gauge error for each segment of the workpiece leaving the second roll stand, where K(N) is the mill spring modulus of the second roll stand, and where P(N) is the determined plasticity for each workpiece segment. 